A finite element for soft tissue deformation based on the absolute nodal coordinate formulation

Obrezkov, Leonid P.; Matikainen, Marko K.; Harish, Ajay B.

doi:10.1007/s00707-019-02607-4

Cited by 29 publications

(9 citation statements)

References 43 publications

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“…Description of an ANCF element's strain energy in the spatial elasticity is a crucial distinction between ANCF and the GEB formulation, which relies on the one-dimensional elastic line theory. Thereby, the incorporation of the nonlinear material models into the ANCF becomes more feasible [31,32]. Whether the strain energy of an ANCF element is derived in terms of the components of the generalized spatial strains [33], or with respect to the components of the deformation gradient [34,35], the ANCF exhibits the features that are typically recognized in the solid element types.…”

Section: Introductionmentioning

confidence: 99%

A contact description for continuum beams with deformable arbitrary cross-section

Bozorgmehri

Obrezkov²,

Harish³

et al. 2023

Finite Elements in Analysis and Design

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Section: Introductionmentioning

confidence: 99%

A contact description for continuum beams with deformable arbitrary cross-section

Bozorgmehri

Obrezkov²,

Harish³

et al. 2023

Finite Elements in Analysis and Design

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“…This approach leads to the finite element discretization over the subtendon's length and makes it possible to consider material laws based on the continuum mechanics. Recent studies [14][15][16][17] show that this transition is possible without significant losses in the quality of the results within the ANCF framework. For example, the work [16] considers the deformations of the beam-like structures described with the ANCF continuum beam elements and from the various soft material models.…”

Section: Introductionmentioning

confidence: 99%

Modeling of the Achilles Subtendons and Their Interactions in a Framework of the Absolute Nodal Coordinate Formulation

2022

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Experimental results have revealed the sophisticated Achilles tendon (AT) structure, including its material properties and complex geometry. The latter incorporates a twisted design and composite construction consisting of three subtendons. Each of them has a nonstandard cross-section. All these factors make the AT deformation analysis computationally demanding. Generally, 3D finite solid elements are used to develop models for AT because they can discretize almost any shape, providing reliable results. However, they also require dense discretization in all three dimensions, leading to a high computational cost. One way to reduce degrees of freedom is the utilization of finite beam elements, requiring only line discretization over the length of subtendons. However, using the material models known from continuum mechanics is challenging because these elements do not usually have 3D elasticity in their descriptions. Furthermore, the contact is defined at the beam axis instead of using a more general surface-to-surface formulation. This work studies the continuum beam elements based on the absolute nodal coordinate formulation (ANCF) for AT modeling. ANCF beam elements require discretization only in one direction, making the model less computationally expensive. Recent work demonstrates that these elements can describe various cross-sections and materials models, thus allowing the approximation of AT complexity. In this study, the tendon model is reproduced by the ANCF continuum beam elements using the isotropic incompressible model to present material features.

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“…Some of the most recent developments include enhancements in numerical performance [14,18,20,34]. Applications of the ANCF include soft machines [13], biological tissues [29,30], cables and wires [12,19], pneumatic elements [37], dielectric elastomer actuators [24], railroad track structures [33], and rotating shafts [4]. As these applications imply, the ANCF is especially useful when analyzing beam-or plate-like structures that experience large deformations and large rotations.…”

Section: Introductionmentioning

confidence: 99%

Analysis of electromechanical systems based on the absolute nodal coordinate formulation

et al. 2022

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The absolute nodal coordinate formulation (ANCF) approach has been successfully used to analyze bodies undergoing large deformations in multibody dynamics applications. In this study, the ANCF is extended to the analysis of coupled electromechanical systems. To this end, the electrostatic equations are solved by means of conventional plane finite elements, and the ANCF is used to describe the geometrically nonlinear elastic deformation of a thin beam. Bidirectional coupling between electrostatic and elastic domains was introduced using an iterative staggering algorithm. The results illustrate that the ANCF approach can be applied to electromechanical problems when objects are discretized using beam and plate elements. Two numerical examples of microbeams subject to an electrostatic field are used to validate the proposed solution strategy and to reveal characteristic features of fully coupled electromechanical solutions accounting for finite strain theory.

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A finite element for soft tissue deformation based on the absolute nodal coordinate formulation

Cited by 29 publications

References 43 publications

A contact description for continuum beams with deformable arbitrary cross-section

A contact description for continuum beams with deformable arbitrary cross-section

Modeling of the Achilles Subtendons and Their Interactions in a Framework of the Absolute Nodal Coordinate Formulation

Analysis of electromechanical systems based on the absolute nodal coordinate formulation

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